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Acta Mathematicae Applicatae Sinica English Series

Construction of a Class of Quantum Boolean Functions Based on the Hadamard Matrix

Jiao Jiao, Du, Shan-qi, Pang, Qiaoyan, Wen Wen, Jie Jie, Zhang

Published Jan 1, 2015• 0 citations
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Abstract

In this study, a new methodology based on the Hadamard matrix is proposed to construct quantum Boolean functions f such that f = I2n-2P2n, where I2n is an identity matrix of order 2n and P2n is a projective matrix with the same order as I2n. The enumeration of this class of quantum Boolean functions is also presented.

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This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and nonadditive quantum error correcting codes. The new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original ((5, 6, 2)) code found by Rains It also extends to operator quantum error correcting codes.
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